Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Algorithm for computation of Zernike polynomials expansion coefficients

Not Accessible

Your library or personal account may give you access

Abstract

A numerically efficient algorithm for expanding a function in a series of Zernike polynomials is presented. The algorithm evaluates the expansion coefficients through the standard 2-D integration formula derived from the Zernike polynomials’ orthogonal properties. Quadratic approximations are used along with the function to be expanded to eliminate the computational problems associated with integrating the oscillatory behavior of the Zernike polynomials. This yields a procedure that is both fast and numerically accurate. Comparisons are made between the proposed scheme and a procedure using a nested 2-D Simpson’s integration rule. The results show that typically at least a fourfold improvement in computational speed can be expected in practical use.

© 1989 Optical Society of America

Full Article  |  PDF Article
More Like This
Analytical method for the transformation of Zernike polynomial coefficients for scaled, rotated, and translated pupils

Lei Li, Bao Zhang, Yongsen Xu, and Dejiang Wang
Appl. Opt. 57(34) F22-F30 (2018)

Zernike expansion of derivatives and Laplacians of the Zernike circle polynomials

A. J. E. M. Janssen
J. Opt. Soc. Am. A 31(7) 1604-1613 (2014)

Wave-front interpretation with Zernike polynomials

J. Y. Wang and D. E. Silva
Appl. Opt. 19(9) 1510-1518 (1980)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (7)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (43)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved